Neutrino Oscillation as the Unique Admissible Reconstruction of Flavor Under Noncommuting Propagation

This paper develops a reconstruction-theoretic account of neutrino oscillation as a structural consequence of admissible boundary-to-boundary witness preservation under coherent PMNS propagation. Rather than proposing new neutrino dynamics or modifying the Standard Model, the paper analyzes the status of weak-flavor identity within a constrained reconstruction framework. Weak flavor is treated as a boundary-defined witness fixed by charged-current interaction events, not as a globally transported propagation-invariant label. Core contribution The central result is that globally transported weak-flavor identity cannot be admissibly totalized over the propagation interior. Formally, weak-flavor transport is represented as a partial boundary operator whose domain is fixed by admissible detector-accessible witness structure. Any attempt to extend that operator across the propagation carrier either: changes the physical witness algebra, collapses to bookkeeping equivalence, or instantiates an inadmissible reconstruction obstruction. Formal framework The manuscript introduces: a partial PMNS reconstruction category, a universal reconstruction quotient, an internal admissible-totalization obstruction, and a boundary-functional AQFT-compatible embedding. Within this framework, standard oscillatory boundary-to-boundary reconstruction is shown to be the unique admissible reconstruction class up to witness-preserving bookkeeping equivalence. Broader significance The broader implication is methodological. Beyond-Standard-Model neutrino proposals should be assessed by whether they introduce new admissible witnesses, such as: altered transition functionals, new detector couplings, matter-effect deviations, non-unitarity signatures, sterile-sector leakage, decoherence patterns, or other boundary-accessible reconstruction changes. They should not receive structural standing merely by adding hidden interior ontology while preserving all PMNS observables. Scope No new oscillation parameters, phenomenological fits, or empirical deviations are proposed. The contribution is classificatory and structural: it supplies an operator-domain obstruction and reconstruction criterion for distinguishing admissible BSM extensions from hidden flavor-transport bookkeeping. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility